Common fixed points for PD-operators on probabilistic metric space

Year 2015, Volume: 28 Issue: 3, 457 - 463, 30.01.2015

Arvind Bhatt

https://izlik.org/JA68FC57HE

Abstract

In this paper, we obtain some common fixed point theorems for recently introduced notion of PD-operators on a set X equipped with the function F without using the triangle inequality besides relaxing symmetric condition. Our results extend the results of Pathak and Rai [Common fixed points for PD-operator pairs under relaxed conditions with applications, Journal of Computational and Applied Mathematics 239(1)(2013) 103-113], Hussain et al.[Common fixed points for JH-operators and occasionally weakly biased pairs under relaxed conditions, Nonlinear Anal.74(2011) 2133-2140], Bhatt et al.[Common Fixed point theorems for occasionally weakly compatible mappings under relaxed conditions, Non-linear analysis Theory, Methods and appl. 73(2010) 176-182] and several others.

Keywords

Probabilistic metric space , PD-operator , fixed point theorem.

References

• Wilson, W.A., On semi metric spaces, Amer.J.Math.53 (1931), 361-373. [2] Menger, K. Statistical metrices, Nat. Acad.Sci.USA. 28(1942) 535-537.